BUILT-IN MATHEMATICA SYMBOL

ReflectionMatrix

ReflectionMatrix[v]
gives the matrix that represents reflection of points in a mirror normal to the vector v.

MORE INFORMATION

The reflection is in a mirror that goes through the origin.

ReflectionMatrix works in any number of dimensions. In 2D it reflects in a line; in 3D it reflects in a plane.

EXAMPLES

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Basic Examples (2)

Reflect along the

axis, or equivalently reflect in the

axis:

Reflect along the vector

or equivalently in the plane given by

:

Reflect along the

axis, or equivalently reflect in the

axis:

In[1]:=

Out[1]//MatrixForm=

In[2]:=

Out[2]=

Reflect along the vector

or equivalently in the plane given by

:

In[1]:=

Out[1]//MatrixForm=

Scope (4)

Reflect along the vector

or equivalently in the plane given by

:

Points in the reflection plane remain fixed:

Points outside the reflection plane get reflected in the plane:

Reflection matrix for symbolic unit vector

:

Vectors normal to

remain unchanged:

Transformation applied to a 2D shape:

Transformation applied to a 3D shape:

Applications (1)

Flipping a surface:

Properties & Relations (3)

The determinant of a reflection matrix is

:

The inverse of a reflection matrix is the matrix itself:

Reflection can be thought of as a special case of scaling:

Possible Issues (1)

Reflection changes the orientation of polygons:

Neat Examples (1)

Reflections of a cuboid in vertical planes: